How can I construct a numeral system that represents the real numbers on a logarithmic scale?

Question

I recently read this relatively old article, which argues that humans, along with most animals, have an innate intuition for logarithms, and tend to imagine numbers in a logarithmic, rather than linear way.

This seems to imply that children need to "un-learn" their intuition for logarithms when being taught standard base counting. So, my question is:

As an alternative to the linear "base-10" counting system, is there a numeral system capable of representing the real numbers on a logarithmic scale (possibly using different symbols), that may be more intuitive for humans to understand?

Answer 1

Interesting question. The article suggests that the logarithmic perception built into the nervous system is for the intensity of a stimulus. But the numbers we write down are for counting things - and they are usually small numbers.

When scientists need to grapple with numbers that cover a large range (near $0$ to very large) they use scientific notation, which is in effect logarithmic.

Answer 2

Is the current system really "linear", though?

The length of a number (when written down) is actually approximatelly the logarithm (base $10$) of the number, which is why in a way, $10000$ is closer to $100000$ than it is to $100$...